A Fully Compressed Algorithm for Computing the Edit Distance of Run-Length Encoded Strings

Chen, Kuan‐Yu; Chao, Kun-Mao

doi:10.1007/978-3-642-15775-2_36

Cited by 4 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example the s-factorization of the string S = abaabababaaaaabbabab is a, b, a, aba, baba, aaaa, b, babab. This can be represented as a, b, (1, 1), (1, 3), (5,4), (10,4), (2, 1), (5,5). In this paper, we will focus on describing algorithms that output only the length of each factor of the s-factorization, but it is not difficult to modify them to output the previous position as well, in the same time and space complexities.…”

Section: Lz Encodingsmentioning

confidence: 99%

“…Many efficient algorithms that deal with RLE versions of classical problems on strings have been proposed in the literature (e.g. : exact pattern matching [2,4,7], approximate matching [3,26], edit distance [5,8,10,24], longest common subsequence [17,25], rank/select structures [22], palindrome detection [11]). In this paper, we consider the problem of computing the Lempel-Ziv factorization (LZ factorization) of a string via RLE.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time and Space Efficient Lempel-Ziv Factorization based on Run Length Encoding

Yamamoto,

Bannai,

Inenaga

et al. 2012

Preprint

View full text Add to dashboard Cite

We propose a new approach for calculating the Lempel-Ziv factorization of a string, based on run length encoding (RLE). We present a conceptually simple off-line algorithm based on a variant of suffix arrays, as well as an on-line algorithm based on a variant of directed acyclic word graphs (DAWGs). Both algorithms run in O(N + n log n) time and O(n) extra space, where N is the size of the string, n ≤ N is the number of RLE factors. The time dependency on N is only in the conversion of the string to RLE, which can be computed very efficiently in O(N ) time and O(1) extra space (excluding the output). When the string is compressible via RLE, i.e., n = o(N ), our algorithms are, to the best of our knowledge, the first algorithms which require only o(N ) extra space while running in o(N log N ) time.

show abstract

Section: Lz Encodingsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time and Space Efficient Lempel-Ziv Factorization based on Run Length Encoding

Yamamoto,

Bannai,

Inenaga

et al. 2012

Preprint

View full text Add to dashboard Cite

show abstract

“…Gold and Sharir [14] showed a subquadratic O(n 2 log log log n/ log log n)-time algorithm for arbitrary time series and Kuszmaul [21] developed an O(n • dtw(x, y))-time algorithm assuming that the minimum nonzero local cost is one. Notably, specialized algorithms for other string problems on run-length encoded strings have also been studied recently, for example, for Longest Common Subsequence [5,28] and Edit Distance [9,10], which have applications in sequence alignment in bioinformatics. Our Contributions.…”

Section: Introductionmentioning

confidence: 99%

Fast Exact Dynamic Time Warping on Run-Length Encoded Time Series

et al. 2022

View full text Add to dashboard Cite

Dynamic Time Warping (DTW) is a well-known similarity measure for time series. The standard dynamic programming approach to compute the DTW distance of two length-n time series, however, requires $$O(n^2)$$ O ( n 2 ) time, which is often too slow for real-world applications. Therefore, many heuristics have been proposed to speed up the DTW computation. These are often based on lower bounding techniques, approximating the DTW distance, or considering special input data such as binary or piecewise constant time series. In this paper, we present a first exact algorithm to compute the DTW distance of two run-length encoded time series whose running time only depends on the encoding lengths of the inputs. The worst-case running time is cubic in the encoding length. In experiments we show that our algorithm is indeed fast for time series with short encoding lengths.

show abstract